LHC Predictions1 from an extended
theory2 with Elastic, Inelastic, and Path
Length Fluctuating Jet Energy Loss
William Horowitz
Department of Physics, Columbia University
538 W 120th St., New York, NY 10027, USA
Frankfurt Institute for Advanced Studies (FIAS)
60438 Frankfurt am Main, Germany
November 15, 2006
1. W.Horowitz et al to be published
2. S.Wicks, W.Horowitz, M.Djordjevic and M.Gyulassy, nucl-th/0512076 v3, NPA in press
With thanks to Azfar Adil and Carsten Greiner
11/15/06
William Horowitz
1
Outline
• Energy dependence of jet quenching at
the LHC as a test of loss mechanisms
– Highly distinct LHC RAA(pT) predictions
– Naturalness of the difference
• Intro to Physics of Nothing
– P0 = Exp(-Nc), the probability of no jet
interactions. Nc ~ selrL is the average
number of elastic collisions
11/15/06
William Horowitz
2
Modeling Energy Loss
– Different models include some effects while
neglecting others
• Radiative only loss:
(AWS, Majumder, Vitev)
• Convolved radiative and elastic loss (WHDG)
• Inclusion of probability of nothing (separate from
probability of emitting no radiation, Pg0!)
– Nc is the number of elastic collisions suffered while propagating out
11/15/06
William Horowitz
3
Probability of Overquench: DE > E
– For highly suppressed jets, P(e > 1) has a
large support for overabsorption. One of
two choices is generally made:
• Renormalize (reweight) uniformly
• Include an explicit d(1-e) term
– We always use the latter
11/15/06
William Horowitz
4
Our Extended Theory
• Convolve Elastic with Inelastic energy
loss fluctuations (
)
• Include path length fluctuations in
diffuse nuclear geometry with 1+1D
Bjorken expansion
11/15/06
William Horowitz
5
Simplified Treatment Uses Fixed L
– Estimates of a fixed, single, representative length:
where
and the fitted L is found by varying it until it best
reproduces the true geometric average.
• There is no a priori method to determine how much the
first two deviate from the actual answer
11/15/06
William Horowitz
6
Path Length Fluctuations
Can Not be Neglected
• P(L) is a wide
distribution
– Flavor
independent
• Flavor dependent
best fixed length
approximation
LQ’s not a priori
obvious
11/15/06
S. Wicks, WH, M. Gyulassy, and M. Djordjevic, nucl-th/0512076
William Horowitz
7
RHIC p Results
• Inclusion of both fluctuating
elastic loss and paths is
essential to reproduce data
– Fully perturbative
– dNg/dy = 1000 consistent with
entropy data for conservative
as = .3
• Results are sensitive to
changes in dNg/dy and as
– Model is not “fragile”
– Running of as will be an
important effect
11/15/06
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
William Horowitz
8
Suppression of AWS
• AWS pQCD-based controlling parameter
nonperturbatively large to fit RHIC data
must be
-pQCD gives = c e3/4, where c ~ 2; c ~ 8-20 required for RHIC data
-Needed because radiative only energy loss (and
> 1? R = (1/2) L3)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A. Wiedemann,
Nucl. Phys. A747:511:529 (2005)
11/15/06
William Horowitz
9
LHC p Predictions
WH, S. Wicks, M. Gyulassy, M. Djordjevic,
in preparation
11/15/06
• Our predictions show a
significant increase in RAA as a
function of pT
• This rise is robust over the
range of predicted dNg/dy for
the LHC that we used
• This should be compared to
the flat in pT curves of AWSbased energy loss (next slide)
• We wish to understand the
origin of this difference
William Horowitz
10
Comparison of LHC p Predictions
(a)
(b)
K. J. Eskola, H. Honkanen, C. A. Salgado, and U. A.
Wiedemann, Nucl. Phys. A747:511:529 (2005)
A. Dainese, C. Loizides, G. Paic, Eur. Phys. J. C38:461474 (2005)
Curves of AWS-based energy loss are flat in pT
11/15/06
William Horowitz
11
Why AWS is Flat
• Flat in pT curves result from extreme suppression at the
LHC
– When probability leakage P(e > 1) is large, the (renormalized or not)
distribution becomes insensitive to the details of energy loss
• Enormous suppression due to:
– Already (nonperturbatively) large suppression at RHIC for AWS
– Extrapolation to LHC assumes 7 times RHIC medium densities (using
EKRT)
» Note: even if LHC is only ~ 2-3 times RHIC,
still an immoderate ~ 30-45
• As seen on the previous slide, Vitev predicted a similar
rise in RAA(pT) as we do
– Vitev used only radiative loss, Prad(e), but assumed fixed path
– WHDG similar because elastic and path fluctuations compensate
11/15/06
William Horowitz
12
The Rise of GLV Rad+El+Geom
• Use of both Prad AND Pel implies neither has much weight for
DE > E at RHIC
• For the dNg/dy values used, high-pT jets at the LHC have
asymptotic energy loss: DErad/E ~ a3 Log(E/m2L)/E
DEel/E ~ a2 Log((E T)1/2/mg)/E
WH, S. Wicks, M. Gyulassy, M. Djordjevic, in preparation
• LHC RAA(pT) dependence caused by deceasing energy loss not
altered by the flat production spectra
11/15/06
William Horowitz
13
Probability of No Energy Loss
• Induced radiative energy loss requires at least one jet
interaction in medium with probability
• After at least one elastic collision, the total energy loss
is a convolution of the momentum lost to the radiated
glue as well as to the scattering centers
– Prad(e) also contains a P(Ng = 0) d(e) due to the probability of no glue
emission
– For fixed as = .3, including P0 physics accounts for 50% of RAA
– Allowing as(T) to run as as(q2=2pT(z)) reduces P0 by a factor of 2
– Integration over momentum transfers with as(q2) given by vacuum
running formally gives P0=0
11/15/06
William Horowitz
14
Conclusions
• LHC RAA(pT) data will distinguish between
energy loss models
– GLV Rad+El+Geom predicts significant rise in pT
– AWS type models predict flat pT dependence
• Moderate opacity (GLV, WW) RAA predictions
sensitive to noninteracting free jets
RAA ~ P0 + (1-P0) RAA(Nc>0), P0 = exp(-selrL)
11/15/06
William Horowitz
15